Multiple Positive Solutions of m-Point BVPs for Third-Order p-Laplacian Dynamic Equations on Time Scales

This paper is concerned with the existence of multiple positive solutions for the third-order pLaplacian dynamic equation φp uΔ∇ t ∇ a t f t, u t , uΔ t 0, t ∈ 0, T T with the multipoint boundary conditions uΔ 0 uΔ∇ 0 0, u T B0 ∑m−2 i 1 biu Δ ξi 0, where φp u |u|p−2u with p > 1. Using the fixed point theorem due to Avery and Peterson, we establish the existence criteria of at least three positive solutions to the problem. As an application, an example is given to illustrate the result. The interesting points are that not only do we consider third-order p-Laplacian dynamic equation but also the nonlinear term f is involved with the first-order delta derivative of the unknown function.